A square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the square, in inches?

[asy]
draw((0,0)--(0,5)--(5,5)--(5,0)--cycle);
draw((1,0)--(1,5));
draw((2,0)--(2,5));
draw((3,0)--(3,5));
draw((4,0)--(4,5));
[/asy]
Let $s$ be the side length of the square.  Then the dimensions of each rectangle are $s\times\frac{s}{5}$.  The perimeter of one of the rectangles is $s+\frac{s}{5}+s+\frac{s}{5}=\frac{12}{5}s$.  Setting $\frac{12}{5}s=36$ inches, we find $s=15$ inches.  The perimeter of the square is $4s=4(15\text{ in.})=\boxed{60}$ inches.